you could ask your private school to allow the parents to pay ALL the fees leftover in full before the election so they cant charge you VAT.
I'm not an expert, or even an informed non-expert, on these matters but there is a tax lawyer on Twitter whom I follow called Dan Neidle. I suspect I'm probably one of the last people to discover him, but I find him fascinating on these matters.
His take is that there will be a lot less tax raised for reasons like you mention here, the fact that schools can claim VAT back etc. and that we'll see a lot of legitimate tax schemes used by schools to minimise this.
For example, if the schools set up an off-shore company to hold their intellectual property which could include obvious stuff like the school brand (Eton, Harrow) but also could include lesson plans, lesson content etc.
Then the schools invoice the parents directly from abroad (without VAT as overseas) for these IP based services and the school only invoices directly (with VAT) for stuff in the UK.
Salaries, building costs etc. And many of these costs will have VAT as both input and output.
Now you've massively reduced the VAT aspect part of the fees.
Now I'm not saying this will reduce the bill to zero but there must be a lot of clever lawyers working on schemes just like this.
In the same way that Switzerland is the world's leading coffee exporter (big firms routing stuff via there) could the Cayman Islands become the independent school capital of the world?
I'm just thinking aloud but it's going to be interesting to see how all this plays out.